Interactive Tutorial

We will now set up the equations for the sample problem, or others, and run some rather fancy programs to solve them.


  1. Look at the diagram above and try writing down the two (2) equations which describe the geometry.
  2. Look at the diagram above and try writing down the four (4) equations which describe the balance of horizontal and vertical forces at each sphere.
  3. If you need help, we'll give you a Hint.
  4. Check your equations with those we deduced (in conference with a number of experts).
  5. Look at the bunch of boxes below. It's nothing more than a simple-minded form being used to enter our equations of statics into the computer.
    6. cosA1 + cosA2 + cosA3 + sinA1 + sinA2 + sinA3 =
    cosA1 + cosA2 + cosA3 + sinA1 + sinA2 + sinA3 =
    T1cosA1 + T2cosA2 + T3cosA3 + T1sinA2 + T2sinA2 + T3sinA3 =
    T1cosA1 + T2cosA2 + T3cosA3 + T1sinA1 + T2sinA2 + T3sinA3 =
    T1cosA1 + T2cosA2 + T3cosA3 + T1sinA1 + T2sinA2 + T3sinA3 =
    T1cosA1 + T2cosA2 + T3cosA3 + T1sinA1 + T2sinA2 + T3sinA3 =



    Outside each box is one of the variables from our problem (tensions and sines and cosines of the angles). Inside each box is the coefficient multiplying it in the equations, or the right-hand side of the equation.

  6. Check that the coefficients of the variables in the boxes agrees with those of the actual equations. If they are wrong, or if you want to solve a problem with different masses and sizes, you can change the numbers in the boxes.
  7. If you make any changes to this form, you can get back to the numbers we entered there originally by pressing the "Clear Form" button:
  8. Now you can ask the computer to search for a solution to these equations.
    (The method it uses is described in the Method section of this document.)

  9. When you press the "Find Solution", the numbers in the form are sent back to our computer in the Department of Physics of Oregon State University, and a Fortran program is executed on a high performance computer. If all goes well, you should get the answers back after waiting a while. Go ahead and try it!
  10. If you change the values in the boxes enough, the equations may end up describing an unphysical situation and the computer will not be able to find a solution. In that case you will be given a bunch of error messages from the computer which may look like

    ***MESSAGE FROM ROUTINE SNSQ IN LIBRARY SLATEC. ***POTENTIALLY RECOVERABLE ERROR, PROG ABORTED, TRACEBACK REQUESTED * ITERATION NOT MAKING GOOD PROGRESS. * ERROR NUMBER = 1 * ***END OF MESSAGE ***JOB ABORT DUE TO UNRECOVERED ERROR. 0 ERROR MESSAGE SUMMARY LIBRARY SUBROUTINE MESSAGE START NERR LEVEL COUNT SLATEC SNSQ ITERATION NOT MAKING 1 1 1

    So you see, that while the computer does not yell at you for messing up, it doesn't exactly tell you anything useful either!

    11. But remember, you can always press the "Clear Form" button to get back to the original numbers, and no one but you will know that you made our very smart computer fail!

  11. Now try some exploration.


Back to Problem